Geom 2point4
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- The document discusses properties from algebra that can be used for reasoning, including addition, subtraction, multiplication, division, equality, and distribution properties. - It also discusses properties of length and measure that can be used to justify segment and angle relationships, including reflexive, symmetric, and transitive properties for both segment length and angle measure. - Examples are provided to illustrate using properties of equality and from algebra to solve equations and justify geometric relationships.
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Geom 2point4
- 1. 2.4 Reasoning with Properties from Algebra Objectives: - Use properties from algebra - Use properties of length and measure to justify segment and angle relationships
- 2. Addition Properties Review Addition Property Subtraction Property Multiplication Property Division Property If a=b, then a+c = b+c If a=b, then a-c = b-c If a = b, then ab = bc If a = b and c ≠ 0, then a/b = b/c
- 3. Addition Properties Review Reflexive Property Symmetric Property Transitive Property Substitution Property For any real number a, a=a If a = b, then b = a If a=b and b=c, then a=c If a = b, then a can be substituted for b in any equation or expression
- 4. Distributive Property Properties of equality along with other properties from algebra, such as the distributive property a(b + c) = ab + ac can be used to solve equations.
- 5. Writing Reasons Look at page 96, Example 1 You all know how to do the algebra. Notice, however, how a reason is listed for each step. This is the basis of doing proofs
- 6. Properties of Equality Segment Length For any segment AB, AB=AB If AB = CD, then CD = AB If AB = CD and CD = EF, then AB = EF Angle Measure For any angle A, m _ A = m _ A If M _ A = m _ B, then m _ B = m _ A If m _ A = m_ B and m_ B = m _ C, then m _ A = M_C Reflexive Symmetric Transitive
- 7. Look at page 98 Example 4 Example 5 Do p. 99 1-9